The Associative Property states that the grouping of numbers does not affect the result when adding or multiplying.
You can apply the Associative Property to expressions that involve addition or multiplication, where the numbers can be regrouped without changing the outcome.
Let's analyze the provided expressions:
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\((9 \cdot 5) \cdot (8 \cdot 3)\): This involves multiplication of two grouped terms. You can apply the Associative Property here since you can regroup the factors.
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\((9 \cdot 5) + 8 + 3\): This involves addition but can also be grouped differently. The Associative Property applies here as well.
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\((5 + 8) \cdot 3\): This is multiplication but does not involve different groupings of the same operation; it’s just one grouping. The Associative Property isn't applicable in a way that changes the expression.
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\((5 \cdot 8) + 3\): This involves addition but again isn't a case for applying the Associative Property since the expression doesn't feature a change in grouping.
The expressions that can be rewritten using the Associative Property are:
- \((9 \cdot 5) \cdot (8 \cdot 3)\)
- \((9 \cdot 5) + 8 + 3\)
So, the first two responses could be rewritten using the Associative Property.